Tone Generation in Cocoa Touch

You could always start with sin waves. :-)

#include <cmath>typedef double Sample;typedef double Time;class MonoNote {protected:    Time start, duration;    virtual void internalRender(double now, Sample *mono) = 0;public:    MonoNote(Time s, Time d) : start(s), duration(d) {}    virtual ~MonoNote() {}    void render(double now, Sample *mono) {        if (start <= now && now < start + duration) {            internalRender(now, mono);        }    }};class MonoSinNote : public MonoNote {    Time freq;    Sample amplitude;protected:    void internalRender(double now, Sample *mono) {        const double v = sin(2*M_PI*(now - start) * freq);        *mono += amplitude*v;    }public:    MonoSinNote(Time s, Time d, Time f, Sample a) : MonoNote(s, d), freq(f), amplitude(a) {}    ~MonoSinNote() {}};

Piano is strange. Robert Moog wrote about it in Keyboard Magazine in March 1980. The fundamental (lowest frequency partial) is in tune, but each higher harmonic is brighter (or "sharper" or higher-pitched) than it should be, and by an increasing amount.

The second through ninth harmonics are louder than the fundamental. The tenth through twentieth are about as loud.

The fundamental swells up in volume and then dives, then it comes back. The other partials have characteristic up and down shapes. The partials exchange energy so the overall volume acts as you would expect. Buts it's a swarm of partials trading energy. I'd guess if you got the lowest few right and the weird inharmonic spread right you'd do OK.

You could watch the action in a software spectrum analyzer and learn what you need to know. Additive synthesis is probably how I'd take on the problem.

Check out Mobilesynth...an open source synthesizer in the app store: http://code.google.com/p/mobilesynth/